This is an induction motor question: why even when we increase the synchronous speed, the slip still remains it's value?
When a variable frequency drive (VFD) supplies power to an induction motor the relationship between the supplied frequency and voltage is usually controlled in a manner that will assure that the operating torque is proportional to slip. The drive system is thus able to provide the same torque at any operating speed in the normal operating range. The slip in RPM or radians per second (not percent) has a constant value for any given torque. The operating range for such operation is usually from the motor's nameplate frequency and voltage to some lower frequency and voltage. The operating range can extend above the nameplate frequency and voltage rating if the motor can tolerate speeds and voltages above the nameplate values. Many standard motors have some capability in that range. Custom-designed motors are available with capabilities that fare exceed the capabilities of standard motors.
VFDs can also be configured to provide operation above the motor's design frequency with constant power and decreasing torque or decreasing power and torque. That type of operation provides a wider total operating speed range. That performance is generally similar to the performance of an internal combustion engines with a variable gear-ratio transmission.
See also: Condition for max torque